Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T10:14:50.310Z Has data issue: false hasContentIssue false
  • English
  • Français

Direction of vorticity and a new regularity criterion for the Navier-Stokes equations

Published online by Cambridge University Press:  17 February 2009

Yong Zhou
Yong Zhou
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, China; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we prove a new regularity criterion in terms of the direction of vorticity for the weak solution to 3-D incompressible Navier-Stokes equations. Under the framework of Constantin and Fefferman, a more relaxed regularity criterion in terms of the direction of vorticity is established.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 3 , January 2005 , pp. 309 - 316
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Caffarelli, L., Kohn, R. and Nirenberg, L., “Partial regularity of suitable weak solutions of the Navier-Stokes equations”, Comm. Pure Appl. Math. 35 (1982) 771–831.CrossRefGoogle Scholar
[2]Constantin, P. and Fefferman, C., “Direction of vorticity and the problem of global regularity for the Navier-Stokes equations”, Indiana Univ. Math. J. 42 (1993) 775–789.CrossRefGoogle Scholar
[3]Hopf, E., “Über die Anfangwertaufgaben fÜr die hydromischen Grundgleichungen”, Math. Nachr. 4 (1951) 213–321.CrossRefGoogle Scholar
[4]Leray, J., “Étude de divers équations intégrales nonlinearies et de quelques problemes que posent l'hydrodinamique”, J. Math. Pures. Appl. 12 (1933) 1–82.Google Scholar
[5]von Wahl, W., The equations of Navier-Stokes and abstract parabolic equations, Aspects of Mathematics E8 (Friedr. Vieweg & Sons, Braunschweig, 1985).CrossRefGoogle Scholar
[6]Zhou, Y., “A new regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component”, Methods Appl. Anal. 9 (2002) 563–578.CrossRefGoogle Scholar
[7]Zhou, Y., “A new regularity criterion of weak solutions to the Navier-Stokes equations”, preprint, 2002.Google Scholar
[8]Zhou, Y., “Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain”, Math. Ann. 328 (2004) 173–192.CrossRefGoogle Scholar